Producing high quality realistic images in reasonable time remains a computer graphics challenge. The goal of a global illumination render is to create a physical image of the steady-state light distribution from a given point of view of a given scene. The rendering equation is usually solved by Monte Carlo numerical integration techniques, as described in the article “The rendering equation” by James T. Kajiya, SIGGRAPH Comput. Graph., 20:143-150, August 1986. In a Monte Carlo renderer, image pixels are computer-generated by averaging the contribution of stochastic rays (random walks, Monte Carlo samples) cast from the camera through the scene.
The principal problem of Monte Carlo rendering is that the variance of the light estimator decreases linearly with the number of stochastic samples. Thus the root mean squared error to an ideal image decreases as the square root of the number of samples. Several hours or even days may be necessary to produce noiseless realistic images. This involves high costs.